sum from n=2 to infinity of 9/(n(n+2))

解答

n = 2 \sum \infty \frac{9}{n ( n + 2 )}

收敛

求解步骤

n = 2 \sum \infty \frac{9}{n ( n + 2 )}

使用常数相乘法则:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 9 \cdot n = 2 \sum \infty \frac{1}{n ( n + 2 )}

使用级数比较审敛法:

收敛

= 9 收敛

= 收敛

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